
where \(\alpha \)  and \(b\)  are modulation specific constants. For
\(M\) -PSK, \(\alpha =1\)  and \(b=\sin ^2(\pi /M)\) . With the aid of [1]} and [2]}, (REF ) is
derived as
\(&{\rm {SER}}_{\gamma _{l|S_{l}},{\textrm {MPSK}}}\\=&\frac{\alpha }{\pi }\sum _{k = 0}^N {\sum _{i = 0}^{m_k - 1}{B_{N,k,i} } } \Gamma \left( {m_k - i} \right)\int _0^{\left( {M - 1}\right)\pi /M}{\left({\frac{b}{{\sin ^2 \theta }} + \frac{m_k}{{a_k }}} \right)^{ - m_k + i} d\theta }\\=&\alpha \sum _{k = 0}^N {\sum _{i = 0}^{m_k - 1} { B_{N,k,i} } }\Gamma \left( {m_k - i} \right)\left( {\frac{{a_k }}{m_k}}\right)^{m_k - i} \left[ \frac{{M - 1}}{M} - \frac{1}{\pi }\sqrt{\frac{{a_k b}}{{a_k b + m_k}}} \left( \left( {\frac{\pi }{2} + \tan ^{-1}\omega } \right)\sum _{p = 0}^{m_k - i - 1}{2p \atopwithdelims ()p}\right.\right.\\&\left.\left.\times \left(4\left( {1 + \frac{{a_kb}}{m_k}}\right)\right)^{-p}+\sin \left({\tan ^{ - 1} \omega }\right)\sum _{p = 1}^{m_k - i - 1}\sum _{t = 1}^{p}T_{p,t}\left(1+\frac{a_k b}{m_k}\right)^{-p}\left({\cos \left( {\tan ^{ -1} \omega } \right)}\right)^{2\left( {p - t} \right) +1}\right)\right],\) 
